Problem: A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters + and 1 into this sequence. For example, sequences (())(), () and (()(())) are regular, while )(, (() and (()))( are not. Let's call a regular bracket sequence "RBS".

You are given a sequence s of n characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

You have to replace every character ? with either ) or ( (different characters ? can be replaced with different brackets). You cannot reorder the characters, remove them, insert other characters, and each ? must be replaced.

Determine if it is possible to obtain an RBS after these replacements.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of one line containing s (2 ≤ |s| ≤ 100) — a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

Output

For each test case, print YES if it is possible to obtain a regular bracket sequence, or NO otherwise}. 

You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).

Example

Input


5
()
(?)
(??)
??()
)?(?


Output


YES
NO
YES
YES
NO

Note

In the first test case, the sequence is already an RBS.

In the third test case, you can obtain an RBS as follows: ()() or (()).

In the fourth test case, you can obtain an RBS as follows: ()().

Solution (in PYTHON3):

Solution:

def valid_brackets(s):
    openBrackets = 0
    for i in s:

        if openBrackets < 0:
            return False

        if i == "(":
            openBrackets += 1
        elif i == ")":
            openBrackets -= 1

    if openBrackets != 0:
        return False

    return True



# # 
# t = int(input())
# for i in range(t):
#     s = input()
#     if len(s) % 2 == 0 and s[0] != ')' and s[-1] != '(':
#         print('YES')
#     else:
#         print('NO')

t = int(input())
for _ in range(t):
    s = input()
    a = list(s)
    count = len(s)//2 -1
    for i in range(len(s)):
        if a[i] == '?':
            if count > 0:
                a[i] = '('
                count -= 1
            else:
                a[i] = ')'
    if valid_brackets(str(a)):
        print("YES")
    else:
        print("NO")